Preprocessing
library(tidyverse)
library(ggdist)
library(ggside)
library(easystats)
library(patchwork)
library(brms)
logmod <- function(x) sign(x) * log(1 + abs(x))
sqrtmod <- function(x) sign(x) * sqrt(abs(x))
cbrtmod <- function(x) sign(x) * (abs(x)**(1 / 3))
perceptual <- read.csv("data/preprocessed_perceptual.csv") |>
mutate(
Block = as.factor(Block),
Illusion_Side = as.factor(Illusion_Side)
)
Ebbinghaus
Error Rate
data <- filter(perceptual, Illusion_Type == "Ebbinghaus")
Descriptive
plot_desc_errors <- function(data) {
data |>
ggplot(aes(x = Illusion_Difference)) +
geom_histogram(data=filter(data, Error == 1),
aes(y=..count../sum(..count..), fill = Illusion_Side),
binwidth = diff(range(data$Illusion_Difference)) / 20, color = "white") +
geom_smooth(aes(y = Error, color = Illusion_Side),
method = 'gam',
formula = y ~ s(x, bs = "cs"),
method.args = list(family = "binomial")) +
scale_x_continuous(expand = c(0, 0)) +
scale_y_continuous(expand = c(0, 0), labels = scales::percent) +
scale_color_manual(values = c("-1" = "#FF5722", "1" = "#43A047")) +
scale_fill_manual(values = c("-1" = "#FF5722", "1" = "#43A047")) +
coord_cartesian(ylim = c(0, 1)) +
labs(x = "Task Difficulty", y = "Probability of Error") +
theme_modern()
}
plot_desc_errors(data)

Model Selection
test_models <- function(data, y = "RT") {
# TODO: add random effect
models <- list()
for(f in c("Illusion_Difference",
"log1p(Illusion_Difference)",
"sqrtmod(Illusion_Difference)",
"cbrtmod(Illusion_Difference)")) {
m <- glmmTMB::glmmTMB(as.formula(paste0(y, "~ ", f, "+ (1|Participant)")),
data = data, family = ifelse(y == "RT", "gaussian", "binomial")
)
models[[f]] <- m
}
performance::test_performance(models)
}
insight::display(test_models(data, "Error"))
| Illusion_Difference |
glmmTMB |
|
| log1p(Illusion_Difference) |
glmmTMB |
0.911 |
| sqrtmod(Illusion_Difference) |
glmmTMB |
0.722 |
| cbrtmod(Illusion_Difference) |
glmmTMB |
0.644 |
Each model is compared to Illusion_Difference.
Model Specification
formula <- brms::bf(
Error ~ Illusion_Difference +
(1 + Illusion_Difference | Participant),
family = "bernoulli"
)
# brms::get_prior(formula, data = data)
# brms::validate_prior(formula)
perceptual_ebbinghaus_err <- brms::brm(formula,
data = data,
refresh = 0
)
## Running MCMC with 4 parallel chains...
##
## Chain 2 finished in 2.0 seconds.
## Chain 1 finished in 2.3 seconds.
## Chain 3 finished in 2.2 seconds.
## Chain 4 finished in 2.2 seconds.
##
## All 4 chains finished successfully.
## Mean chain execution time: 2.2 seconds.
## Total execution time: 2.4 seconds.
save(perceptual_ebbinghaus_err, file="models/perceptual_ebbinghaus_err.Rdata")
Model Inspection
load("models/perceptual_ebbinghaus_err.Rdata")
plot_model_errors <- function(data, model) {
pred <- estimate_relation(model, length = 100)
data |>
ggplot(aes(x = Illusion_Difference)) +
geom_histogram(data=filter(data, Error == 1),
aes(y=..count../sum(..count..)),
binwidth = diff(range(data$Illusion_Difference)) / 20) +
geom_ribbon(data = pred,
aes(ymin = CI_low, ymax = CI_high),
alpha = 1/3, fill = "red") +
geom_line(data = pred,
aes(y = Predicted),
color = "red") +
scale_x_continuous(expand = c(0, 0)) +
scale_y_continuous(expand = c(0, 0), labels = scales::percent) +
coord_cartesian(ylim = c(0, 1)) +
labs(x = "Task Difficulty", y = "Probability of Error") +
theme_modern()
}
plot_model_errors(data, perceptual_ebbinghaus_err)

Response Time
data <- filter(perceptual, Illusion_Type == "Ebbinghaus", Error == 0)
Descriptive
plot_desc_rt <- function(data) {
data |>
ggplot(aes(x = Illusion_Difference, y = RT)) +
# ggpointdensity::geom_pointdensity(size = 3, alpha=0.5) +
# scale_color_gradientn(colors = c("grey", "black"), guide = "none") +
# ggnewscale::new_scale_color() +
stat_density_2d(aes(fill = ..density..), geom = "raster", contour = FALSE) +
scale_fill_gradientn(colors = c("white", "black"), guide = "none") +
ggnewscale::new_scale_fill() +
geom_smooth(aes(color = Illusion_Side, fill = Illusion_Side),
method = 'gam',
formula = y ~ s(x, bs = "cs")) +
scale_color_manual(values = c("-1" = "#FF5722", "1" = "#43A047")) +
scale_fill_manual(values = c("-1" = "#FF5722", "1" = "#43A047")) +
scale_x_discrete(expand = c(0, 0)) +
scale_y_continuous(expand = c(0, 0)) +
labs(x = "Task Difficulty", y = "Response Time (s)") +
theme_modern() +
ggside::geom_ysidedensity(aes(fill = Illusion_Side), color = NA, alpha = 0.3) +
ggside::theme_ggside_void() +
ggside::scale_ysidex_continuous(expand = c(0, 0)) +
ggside::ggside()
}
plot_desc_rt(data)

Model Selection
insight::display(test_models(data, "RT"))
| Illusion_Difference |
glmmTMB |
|
| log1p(Illusion_Difference) |
glmmTMB |
1.18 |
| sqrtmod(Illusion_Difference) |
glmmTMB |
1.72 |
| cbrtmod(Illusion_Difference) |
glmmTMB |
2.01 |
Each model is compared to Illusion_Difference.
Model Specification
# TODO: shift to lognormal
formula <- brms::bf(
RT ~ Illusion_Difference +
(1 + Illusion_Difference | Participant)
)
# brms::get_prior(formula, data = data)
# brms::validate_prior(formula)
perceptual_ebbinghaus_rt <- brms::brm(formula,
data = data,
refresh = 0
)
## Running MCMC with 4 parallel chains...
##
## Chain 4 finished in 2.5 seconds.
## Chain 1 finished in 2.9 seconds.
## Chain 2 finished in 2.8 seconds.
## Chain 3 finished in 3.0 seconds.
##
## All 4 chains finished successfully.
## Mean chain execution time: 2.8 seconds.
## Total execution time: 3.0 seconds.
save(perceptual_ebbinghaus_rt, file="models/perceptual_ebbinghaus_rt.Rdata")
Model Inspection
load("models/perceptual_ebbinghaus_rt.Rdata")
plot_model_rt <- function(data, model) {
pred <- estimate_relation(model, length = 100)
data |>
ggplot(aes(x = Illusion_Difference)) +
stat_density_2d(aes(fill = ..density.., y = RT), geom = "raster", contour = FALSE) +
scale_fill_gradientn(colors = c("white", "black"), guide = "none") +
ggnewscale::new_scale_fill() +
geom_ribbon(data = pred,
aes(ymin = CI_low, ymax = CI_high),
alpha = 1/3, fill = "red") +
geom_line(data = pred,
aes(y = Predicted),
color = "red") +
scale_x_continuous(expand = c(0, 0)) +
scale_y_continuous(expand = c(0, 0)) +
labs(x = "Task Difficulty", y = "Response Time (s)") +
theme_modern()
}
plot_model_rt(data, perceptual_ebbinghaus_rt)

Müller-Lyer
Error Rate
data <- filter(perceptual, Illusion_Type == "MullerLyer")
Descriptive
plot_desc_errors(data)

Model Selection
insight::display(test_models(data, "Error"))
| Illusion_Difference |
glmmTMB |
|
| log1p(Illusion_Difference) |
glmmTMB |
0.955 |
| sqrtmod(Illusion_Difference) |
glmmTMB |
0.778 |
| cbrtmod(Illusion_Difference) |
glmmTMB |
0.684 |
Each model is compared to Illusion_Difference.
Model Specification
formula <- brms::bf(
Error ~ Illusion_Difference +
(1 + Illusion_Difference | Participant),
family = "bernoulli"
)
# brms::get_prior(formula, data = data)
# brms::validate_prior(formula)
perceptual_mullerlyer_err <- brms::brm(formula,
data = data,
refresh = 0
)
## Running MCMC with 4 parallel chains...
##
## Chain 2 finished in 1.9 seconds.
## Chain 1 finished in 2.1 seconds.
## Chain 3 finished in 2.1 seconds.
## Chain 4 finished in 2.2 seconds.
##
## All 4 chains finished successfully.
## Mean chain execution time: 2.1 seconds.
## Total execution time: 2.2 seconds.
save(perceptual_mullerlyer_err, file="models/perceptual_mullerlyer_err.Rdata")
Model Inspection
load("models/perceptual_mullerlyer_err.Rdata")
plot_model_errors(data, perceptual_mullerlyer_err)

Response Time
data <- filter(perceptual, Illusion_Type == "MullerLyer", Error == 0)
Descriptive
plot_desc_rt(data)

Model Selection
insight::display(test_models(data, "RT"))
| Illusion_Difference |
glmmTMB |
|
| log1p(Illusion_Difference) |
glmmTMB |
3.09 |
| sqrtmod(Illusion_Difference) |
glmmTMB |
37.00 |
| cbrtmod(Illusion_Difference) |
glmmTMB |
93.08 |
Each model is compared to Illusion_Difference.
Model Specification
# TODO: shift to lognormal
formula <- brms::bf(
RT ~ cbrtmod(Illusion_Difference) +
(1 + cbrtmod(Illusion_Difference) | Participant)
)
# brms::get_prior(formula, data = data)
# brms::validate_prior(formula)
perceptual_mullerlyer_rt <- brms::brm(formula,
data = data,
refresh = 0
)
## Running MCMC with 4 parallel chains...
##
## Chain 2 finished in 3.8 seconds.
## Chain 4 finished in 3.9 seconds.
## Chain 3 finished in 4.8 seconds.
## Chain 1 finished in 5.1 seconds.
##
## All 4 chains finished successfully.
## Mean chain execution time: 4.4 seconds.
## Total execution time: 5.2 seconds.
save(perceptual_mullerlyer_rt, file="models/perceptual_mullerlyer_rt.Rdata")
Model Inspection
load("models/perceptual_mullerlyer_rt.Rdata")
plot_model_rt(data, perceptual_mullerlyer_rt)

Vertical-Horizontal
Error Rate
data <- filter(perceptual, Illusion_Type == "VerticalHorizontal")
Descriptive
plot_desc_errors(data)

Model Selection
insight::display(test_models(data, "Error"))
| Illusion_Difference |
glmmTMB |
|
| log1p(Illusion_Difference) |
glmmTMB |
0.902 |
| sqrtmod(Illusion_Difference) |
glmmTMB |
0.550 |
| cbrtmod(Illusion_Difference) |
glmmTMB |
0.435 |
Each model is compared to Illusion_Difference.
Model Specification
formula <- brms::bf(
Error ~ Illusion_Difference +
(1 + Illusion_Difference | Participant),
family = "bernoulli"
)
# brms::get_prior(formula, data = data)
# brms::validate_prior(formula)
perceptual_verticalhorizontal_err <- brms::brm(formula,
data = data,
refresh = 0
)
## Running MCMC with 4 parallel chains...
##
## Chain 4 finished in 2.2 seconds.
## Chain 1 finished in 2.4 seconds.
## Chain 2 finished in 2.4 seconds.
## Chain 3 finished in 2.3 seconds.
##
## All 4 chains finished successfully.
## Mean chain execution time: 2.3 seconds.
## Total execution time: 2.5 seconds.
save(perceptual_verticalhorizontal_err, file="models/perceptual_verticalhorizontal_err.Rdata")
Model Inspection
load("models/perceptual_verticalhorizontal_err.Rdata")
plot_model_errors(data, perceptual_verticalhorizontal_err)

Response Time
data <- filter(perceptual, Illusion_Type == "VerticalHorizontal", Error == 0)
Descriptive
plot_desc_rt(data)

Model Selection
insight::display(test_models(data, "RT"))
| Illusion_Difference |
glmmTMB |
|
| log1p(Illusion_Difference) |
glmmTMB |
1.01 |
| sqrtmod(Illusion_Difference) |
glmmTMB |
0.950 |
| cbrtmod(Illusion_Difference) |
glmmTMB |
0.870 |
Each model is compared to Illusion_Difference.
Model Specification
# TODO: shift to lognormal
formula <- brms::bf(
RT ~ Illusion_Difference +
(1 + Illusion_Difference | Participant)
)
# brms::get_prior(formula, data = data)
# brms::validate_prior(formula)
perceptual_verticalhorizontal_rt <- brms::brm(formula,
data = data,
refresh = 0
)
## Running MCMC with 4 parallel chains...
##
## Chain 4 finished in 2.5 seconds.
## Chain 1 finished in 2.6 seconds.
## Chain 2 finished in 2.6 seconds.
## Chain 3 finished in 2.7 seconds.
##
## All 4 chains finished successfully.
## Mean chain execution time: 2.6 seconds.
## Total execution time: 2.8 seconds.
save(perceptual_verticalhorizontal_rt, file="models/perceptual_verticalhorizontal_rt.Rdata")
Model Inspection
load("models/perceptual_verticalhorizontal_rt.Rdata")
plot_model_rt(data, perceptual_verticalhorizontal_rt)

Individual Scores
get_scores <- function(model, illusion="Ebbinghaus") {
family <- insight::find_response(model)
modelbased::estimate_grouplevel(model) |>
data_filter(str_detect(Level, "Participant")) |>
mutate(Group = str_remove(Group, ": Participant"),
Level = str_remove(Level, "Participant.")) |>
select(Group, Participant = Level, Median) |>
pivot_wider(names_from = "Group", values_from = "Median") |>
data_rename("Illusion_Difference",
paste0("Perception_", illusion, "_Difficulty_", family)) |>
data_rename("Intercept",
paste0("Perception_", illusion, "_Intercept_", family))
}
scores <- get_scores(perceptual_ebbinghaus_err, illusion="Ebbinghaus") |>
merge(get_scores(perceptual_ebbinghaus_rt, illusion="Ebbinghaus"), by="Participant") |>
merge(get_scores(perceptual_mullerlyer_err, illusion="MullerLyer"), by="Participant") |>
merge(get_scores(perceptual_mullerlyer_rt, illusion="MullerLyer"), by="Participant") |>
merge(get_scores(perceptual_verticalhorizontal_err, illusion="VerticalHorizontal"), by="Participant") |>
merge(get_scores(perceptual_verticalhorizontal_rt, illusion="VerticalHorizontal"), by="Participant")
write.csv(scores, "data/scores_perceptual.csv", row.names = FALSE)